Subgroups — C₇×#21463 #13198679

Order 1792.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2323	C₂	1	1	yes	maximal, characteristic
6	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1878	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1873	C₂	1	1	yes	maximal, characteristic
9	C₇×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1854	C₂	1	1	yes	maximal, characteristic
12	C₇×#1787	C₂	1	1	yes	maximal, characteristic
13	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₇×#519	—	2	4	no	—
21	C₇×#519	—	2	4	no	—
22	C₂×C₄×C₇×Q₈	—	2	1	no	—
23	C₂×C₄×C₇×Q₈	—	2	1	no	—
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#117	—	2	1	no	—
30	C₂×C₇×#117	—	2	1	no	—
31	C₂×C₇×#117	C₂²	1	1	yes	characteristic
32	C₂×C₇×#117	C₂²	1	1	yes	characteristic
33	C₇×#451	C₄	1	8	yes	complemented
34	C₇×#441	—	2	4	no	—
35	C₄×C₇×Q₁₆	—	2	4	no	—
36	C₂×C₇×#107	C₂²	1	1	yes	characteristic
37	C₂×C₇×#106	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×#103	C₂²	1	1	yes	characteristic
40	C₂×C₇×#103	C₂²	1	1	yes	characteristic
41	C₂×C₇×#103	C₂²	1	1	yes	characteristic
42	C₂×C₇×#103	C₂²	1	1	yes	characteristic
43	C₂×C₇×#103	C₂²	1	1	yes	characteristic
44	C₂×C₇×#103	C₂²	1	1	yes	characteristic
45	C₂×C₇×#103	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₇×#97	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
50	C₇×#391	C₂²	1	1	yes	characteristic
51	C₇×#389	—	2	1	no	—
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#388	—	2	1	no	—
54	C₇×#388	—	2	1	no	—
55	C₇×#387	—	2	1	no	—
56	C₇×#380	C₂²	1	1	yes	characteristic
57	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#340	C₂²	1	1	yes	characteristic
62	C₇×#336	C₂²	1	1	yes	characteristic
63	C₇×#336	C₂²	1	1	yes	characteristic
64	#21463	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂²×C₇×Q₈	—	2	2	no	—
66	C₂²×C₇×Q₈	—	2	2	no	—
67	C₂²×C₇×Q₈	—	2	2	no	—
68	C₂²×C₇×Q₈	—	2	2	no	—
69	C₂²×C₇×Q₈	—	2	1	no	—
70	C₂²×C₇×Q₈	—	2	2	no	—
71	C₂²×C₇×Q₈	C₂×C₄	1	4	yes	—
72	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₇	—	2	1	no	—
76	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₇×Q₁₆	—	2	2	no	—
78	C₂×C₇×Q₁₆	—	2	2	no	—
79	C₂×C₇×Q₁₆	—	2	2	no	—
80	C₂×C₇×Q₁₆	—	2	2	no	—
81	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	—
82	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	—
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₇×C₂²⋊Q₈	—	2	2	no	—
88	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
89	C₄×C₇×Q₈	—	2	8	no	—
90	C₄×C₇×Q₈	—	2	8	no	—
91	C₄×C₇×Q₈	—	2	2	no	—
92	C₄×C₇×Q₈	—	2	2	no	—
93	C₄×C₇×Q₈	—	2	2	no	—
94	C₄×C₇×Q₈	—	2	2	no	—
95	C₄×C₇×Q₈	—	2	2	no	—
96	C₄×C₇×Q₈	—	2	2	no	—
97	C₄×C₇×Q₈	—	2	2	no	—
98	C₄×C₇×Q₈	—	2	2	no	—
99	C₄×C₇×Q₈	D₄	1	4	yes	—
100	C₄×C₇×Q₈	D₄	1	4	yes	—
101	C₇×#117	—	2	8	no	—
102	C₇×#117	—	2	8	no	—
103	C₇×#117	—	2	2	no	—
104	C₇×#117	—	2	2	no	—
105	C₇×#117	—	2	2	no	—
106	C₇×#117	—	2	2	no	—
107	C₂×C₇×C₄⋊C₄	—	2	1	no	—
108	C₂×C₇×C₄⋊C₄	—	2	1	no	—
109	C₂×C₇×C₄⋊C₄	—	2	1	no	—
110	C₂×C₇×C₄⋊C₄	—	2	1	no	—
111	C₂×C₇×C₄⋊C₄	—	2	1	no	—
112	C₂×C₇×C₄⋊C₄	—	2	1	no	—
113	C₂×C₇×C₄⋊C₄	—	2	1	no	—
114	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₇	—	2	1	no	—
127	C₂×C₄²×C₇	—	2	1	no	—
128	C₂×C₄²×C₇	—	2	1	no	—
129	C₂×C₄²×C₇	—	2	1	no	—
130	C₂×C₄²×C₇	—	2	1	no	—
131	C₂×C₄²×C₇	—	2	1	no	—
132	C₂×C₄²×C₇	—	2	1	no	—
133	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
135	C₇×#107	—	2	2	no	—
136	C₇×#106	—	2	2	no	—
137	C₇×#103	—	2	2	no	—
138	C₇×#103	—	2	2	no	—
139	C₇×#103	—	2	2	no	—
140	C₇×#103	—	2	2	no	—
141	C₇×#103	—	2	2	no	—
142	C₇×#103	—	2	2	no	—
143	C₇×#103	C₂×C₄	1	4	yes	—
144	C₇×#103	C₂×C₄	1	4	yes	—
145	C₇×C₂²⋊C₈	—	2	2	no	—
146	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
147	C₇×#97	—	2	2	no	—
148	C₄×C₇×C₈	—	2	2	no	—
149	C₇×#95	—	2	1	no	—
150	C₇×#95	—	2	1	no	—
151	C₇×#95	—	2	1	no	—
152	C₇×#95	—	2	1	no	—
153	C₇×#95	—	2	1	no	—
154	C₂×#519	C₂×C₇	1	1	yes	characteristic
155	C₂×#451	C₂×C₇	1	1	yes	characteristic
156	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
158	#2323	C₂×C₇	1	1	yes	characteristic
159	#1878	C₂×C₇	1	1	yes	characteristic, complemented
160	#1878	C₂×C₇	1	1	yes	characteristic, complemented
161	#1873	C₂×C₇	1	1	yes	characteristic
162	#1865	C₂×C₇	1	1	yes	characteristic, complemented
163	#1863	C₂×C₇	1	1	yes	characteristic, complemented
164	#1854	C₂×C₇	1	1	yes	characteristic
165	#1787	C₂×C₇	1	1	yes	characteristic
166	#1763	C₂×C₇	1	1	yes	characteristic, complemented
167	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
168	#1750	C₂×C₇	1	1	yes	characteristic
169	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₇×Q₈	—	2	4	no	—
171	C₂×C₇×Q₈	—	2	8	no	—
172	C₂×C₇×Q₈	—	2	8	no	—
173	C₂×C₇×Q₈	—	2	4	no	—
174	C₂×C₇×Q₈	—	2	8	no	—
175	C₂×C₇×Q₈	—	2	8	no	—
176	C₂×C₇×Q₈	—	2	4	no	—
177	C₂×C₇×Q₈	—	2	1	no	—
178	C₂×C₇×Q₈	—	2	1	no	—
179	C₂×C₇×Q₈	—	2	1	no	—
180	C₂×C₇×Q₈	—	2	1	no	—
181	C₂×C₇×Q₈	—	2	1	no	—
182	C₂×C₇×Q₈	—	2	1	no	—
183	C₂×C₇×Q₈	—	2	1	no	—
184	C₂×C₇×Q₈	—	2	1	no	—
185	C₂×C₇×Q₈	—	2	1	no	—
186	C₂×C₇×Q₈	—	2	1	no	—
187	C₂×C₇×Q₈	—	2	1	no	—
188	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
189	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
190	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
191	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
192	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
193	C₂×C₇×Q₈	#41	1	2	yes	—
194	C₂×C₇×Q₈	#41	1	2	yes	—
195	C₂²×C₄×C₇	—	2	4	no	—
196	C₂²×C₄×C₇	—	2	4	no	—
197	C₂²×C₄×C₇	—	2	4	no	—
198	C₂²×C₄×C₇	—	2	1	no	—
199	C₂²×C₄×C₇	—	2	1	no	—
200	C₂²×C₄×C₇	—	2	1	no	—
201	C₂²×C₄×C₇	—	2	1	no	—
202	C₂²×C₄×C₇	—	2	1	no	—
203	C₂²×C₄×C₇	—	2	1	no	—
204	C₂²×C₄×C₇	—	2	1	no	—
205	C₂²×C₄×C₇	—	2	1	no	—
206	C₂²×C₄×C₇	—	2	1	no	—
207	C₂²×C₄×C₇	—	2	1	no	—
208	C₂²×C₄×C₇	—	2	1	no	—
209	C₂²×C₄×C₇	—	2	1	no	—
210	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
211	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₇	#41	1	2	yes	—
217	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
218	C₇×Q₁₆	—	2	8	no	—
219	C₇×Q₁₆	—	2	8	no	—
220	C₂×C₇×C₈	—	2	1	no	—
221	C₂×C₇×C₈	—	2	1	no	—
222	C₂×C₇×C₈	—	2	1	no	—
223	C₂×C₇×C₈	—	2	1	no	—
224	C₂×C₇×C₈	—	2	1	no	—
225	C₂×C₇×C₈	—	2	1	no	—
226	C₂×C₇×C₈	—	2	1	no	—
227	C₂×C₇×C₈	—	2	1	no	—
228	C₂×C₇×C₈	—	2	1	no	—
229	C₂×C₇×C₈	—	2	1	no	—
230	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
231	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
232	C₇×C₄⋊C₄	—	2	4	no	—
233	C₇×C₄⋊C₄	—	2	4	no	—
234	C₇×C₄⋊C₄	—	2	4	no	—
235	C₇×C₄⋊C₄	—	2	4	no	—
236	C₇×C₄⋊C₄	—	2	4	no	—
237	C₇×C₄⋊C₄	—	2	2	no	—
238	C₇×C₄⋊C₄	—	2	2	no	—
239	C₇×C₄⋊C₄	—	2	1	no	—
240	C₇×C₄⋊C₄	—	2	1	no	—
241	C₇×C₄⋊C₄	—	2	1	no	—
242	C₇×C₄⋊C₄	—	2	1	no	—
243	C₇×C₄⋊C₄	—	2	1	no	—
244	C₇×C₄⋊C₄	—	2	1	no	—
245	C₇×C₄⋊C₄	—	2	1	no	—
246	C₇×C₄⋊C₄	—	4	2	no	—
247	C₇×C₄⋊C₄	—	8	1	no	—
248	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
249	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
250	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
251	C₇×C₂²⋊C₄	—	2	4	no	—
252	C₇×C₂²⋊C₄	—	2	4	no	—
253	C₇×C₂²⋊C₄	—	2	2	no	—
254	C₇×C₂²⋊C₄	—	2	2	no	—
255	C₇×C₂²⋊C₄	—	8	1	no	—
256	C₄²×C₇	—	2	4	no	—
257	C₄²×C₇	—	2	4	no	—
258	C₄²×C₇	—	2	4	no	—
259	C₄²×C₇	—	2	4	no	—
260	C₄²×C₇	—	2	4	no	—
261	C₄²×C₇	—	2	1	no	—
262	C₄²×C₇	—	2	1	no	—
263	C₄²×C₇	—	4	2	no	—
264	C₄²×C₇	—	8	1	no	—
265	C₄²×C₇	C₂×D₄	1	2	yes	—
266	C₄²×C₇	C₂×D₄	1	2	yes	—
267	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
268	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
269	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
271	#519	—	2	4	no	—
272	#519	—	2	4	no	—
273	C₂×C₄×Q₈	—	2	1	no	—
274	C₂×C₄×Q₈	—	2	1	no	—
275	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
277	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
278	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
280	C₂×#117	—	2	1	no	—
281	C₂×#117	—	2	1	no	—
282	C₂×#117	C₂²×C₇	1	1	yes	characteristic
283	C₂×#117	C₂²×C₇	1	1	yes	characteristic
284	#451	C₄×C₇	1	8	yes	complemented
285	#441	—	2	4	no	—
286	C₄×Q₁₆	—	2	4	no	—
287	C₂×#107	C₂²×C₇	1	1	yes	characteristic
288	C₂×#106	C₂²×C₇	1	1	yes	characteristic
289	C₂×#103	C₂²×C₇	1	1	yes	characteristic
290	C₂×#103	C₂²×C₇	1	1	yes	characteristic
291	C₂×#103	C₂²×C₇	1	1	yes	characteristic
292	C₂×#103	C₂²×C₇	1	1	yes	characteristic
293	C₂×#103	C₂²×C₇	1	1	yes	characteristic
294	C₂×#103	C₂²×C₇	1	1	yes	characteristic
295	C₂×#103	C₂²×C₇	1	1	yes	characteristic
296	C₂×#103	C₂²×C₇	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
299	C₂×#97	C₂²×C₇	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
301	#391	C₂²×C₇	1	1	yes	characteristic
302	#389	—	2	1	no	—
303	#389	C₂²×C₇	1	1	yes	characteristic
304	#388	—	2	1	no	—
305	#388	—	2	1	no	—
306	#387	—	2	1	no	—
307	#380	C₂²×C₇	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
309	#340	C₂²×C₇	1	1	yes	characteristic
310	#340	C₂²×C₇	1	1	yes	characteristic
311	#340	C₂²×C₇	1	1	yes	characteristic
312	#340	C₂²×C₇	1	1	yes	characteristic
313	#336	C₂²×C₇	1	1	yes	characteristic
314	#336	C₂²×C₇	1	1	yes	characteristic
315	C₂³×C₇	—	2	1	no	—
316	C₂³×C₇	—	2	1	no	—
317	C₂³×C₇	—	2	1	no	—
318	C₂³×C₇	—	2	1	no	—
319	C₂³×C₇	—	2	1	no	—
320	C₂³×C₇	—	2	1	no	—
321	C₂³×C₇	C₄×D₄	1	2	yes	—
322	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
323	C₇×Q₈	—	2	16	no	—
324	C₇×Q₈	—	2	2	no	—
325	C₇×Q₈	—	2	2	no	—
326	C₇×Q₈	—	2	2	no	—
327	C₇×Q₈	—	2	2	no	—
328	C₇×Q₈	—	2	2	no	—
329	C₇×Q₈	—	2	2	no	—
330	C₇×Q₈	—	2	2	no	—
331	C₇×Q₈	—	2	2	no	—
332	C₇×Q₈	—	4	1	no	—
333	C₇×Q₈	—	4	1	no	—
334	C₇×Q₈	C₄×D₄	1	4	yes	—
335	C₇×Q₈	C₄×D₄	1	4	yes	—
336	C₂×C₄×C₇	—	2	16	no	—
337	C₂×C₄×C₇	—	2	2	no	—
338	C₂×C₄×C₇	—	2	2	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	2	no	—
341	C₂×C₄×C₇	—	2	1	no	—
342	C₂×C₄×C₇	—	2	2	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	1	no	—
345	C₂×C₄×C₇	—	2	1	no	—
346	C₂×C₄×C₇	—	2	1	no	—
347	C₂×C₄×C₇	—	2	1	no	—
348	C₂×C₄×C₇	—	2	1	no	—
349	C₂×C₄×C₇	—	2	2	no	—
350	C₂×C₄×C₇	—	2	2	no	—
351	C₂×C₄×C₇	—	2	2	no	—
352	C₂×C₄×C₇	—	2	2	no	—
353	C₂×C₄×C₇	—	2	2	no	—
354	C₂×C₄×C₇	—	2	2	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	2	1	no	—
357	C₂×C₄×C₇	—	2	2	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	1	no	—
360	C₂×C₄×C₇	—	2	1	no	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	1	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	—	4	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	—	4	1	no	—
370	C₂×C₄×C₇	—	4	1	no	—
371	C₂×C₄×C₇	—	4	1	no	—
372	C₂×C₄×C₇	—	4	1	no	—
373	C₂×C₄×C₇	—	4	1	no	—
374	C₂×C₄×C₇	—	4	1	no	—
375	C₂×C₄×C₇	—	4	1	no	—
376	C₂×C₄×C₇	—	4	1	no	—
377	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
378	C₂×C₄×C₇	#120	1	2	yes	—
379	C₂×C₄×C₇	#120	1	2	yes	—
380	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
381	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
384	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
385	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
386	C₇×C₈	—	2	2	no	—
387	C₇×C₈	—	2	2	no	—
388	C₇×C₈	—	4	1	no	—
389	C₇×C₈	—	4	1	no	—
390	C₂²×Q₈	—	2	2	no	—
391	C₂²×Q₈	—	2	2	no	—
392	C₂²×Q₈	—	2	2	no	—
393	C₂²×Q₈	—	2	2	no	—
394	C₂²×Q₈	—	2	1	no	—
395	C₂²×Q₈	—	2	2	no	—
396	C₂²×Q₈	C₂×C₄×C₇	1	4	yes	—
397	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
402	C₂×Q₁₆	—	2	2	no	—
403	C₂×Q₁₆	—	2	2	no	—
404	C₂×Q₁₆	—	2	2	no	—
405	C₂×Q₁₆	—	2	2	no	—
406	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	—
407	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	—
408	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
414	C₄×Q₈	—	2	8	no	—
415	C₄×Q₈	—	2	8	no	—
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	—	2	2	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	—	2	2	no	—
424	C₄×Q₈	C₇×D₄	1	4	yes	—
425	C₄×Q₈	C₇×D₄	1	4	yes	—
426	#117	—	2	8	no	—
427	#117	—	2	8	no	—
428	#117	—	2	2	no	—
429	#117	—	2	2	no	—
430	#117	—	2	2	no	—
431	#117	—	2	2	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
460	#107	—	2	2	no	—
461	#106	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#103	—	2	2	no	—
466	#103	—	2	2	no	—
467	#103	—	2	2	no	—
468	#103	C₂×C₄×C₇	1	4	yes	—
469	#103	C₂×C₄×C₇	1	4	yes	—
470	C₂²⋊C₈	—	2	2	no	—
471	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
472	#97	—	2	2	no	—
473	C₄×C₈	—	2	2	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	C₂²×C₇	—	2	2	no	—
480	C₂²×C₇	—	2	2	no	—
481	C₂²×C₇	—	2	2	no	—
482	C₂²×C₇	—	4	1	no	—
483	C₂²×C₇	—	4	1	no	—
484	C₂²×C₇	—	4	1	no	—
485	C₂²×C₇	—	4	1	no	—
486	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
487	C₂²×C₇	C₂×#120	1	1	yes	characteristic
488	C₂²×C₇	#525	1	1	yes	characteristic
489	C₂²×C₇	#577	1	1	yes	characteristic
490	C₂²×C₇	#578	1	1	yes	characteristic
491	C₂²×C₇	#578	1	1	yes	characteristic
492	C₂²×C₇	#578	1	1	yes	characteristic
493	C₄×C₇	—	2	2	no	—
494	C₄×C₇	—	2	2	no	—
495	C₄×C₇	—	2	4	no	—
496	C₄×C₇	—	2	4	no	—
497	C₄×C₇	—	2	2	no	—
498	C₄×C₇	—	4	2	no	—
499	C₄×C₇	—	4	1	no	—
500	C₄×C₇	—	4	2	no	—
501	C₄×C₇	—	4	1	no	—
502	C₄×C₇	—	4	2	no	—
503	C₄×C₇	—	4	2	no	—
504	C₄×C₇	—	8	1	no	—
505	C₄×C₇	—	8	1	no	—
506	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
507	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
508	C₄×C₇	#525	1	1	yes	characteristic
509	C₄×C₇	#525	1	1	yes	characteristic
510	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
511	C₂×Q₈	—	2	4	no	—
512	C₂×Q₈	—	2	8	no	—
513	C₂×Q₈	—	2	8	no	—
514	C₂×Q₈	—	2	4	no	—
515	C₂×Q₈	—	2	8	no	—
516	C₂×Q₈	—	2	8	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
530	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
531	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
532	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
533	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
534	C₂×Q₈	C₇×#41	1	2	yes	—
535	C₂×Q₈	C₇×#41	1	2	yes	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
552	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
554	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
556	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
557	C₂²×C₄	C₇×#41	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
559	Q₁₆	—	2	8	no	—
560	Q₁₆	—	2	8	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
572	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	8	1	no	—
589	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
590	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
591	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	8	1	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	4	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	4	no	—
601	C₄²	—	2	4	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	4	2	no	—
605	C₄²	—	8	1	no	—
606	C₄²	C₂×C₇×D₄	1	2	yes	—
607	C₄²	C₂×C₇×D₄	1	2	yes	—
608	C₂×C₇	—	4	2	no	—
609	C₂×C₇	C₄×#120	1	1	yes	characteristic
610	C₂×C₇	#2947	1	1	yes	characteristic
611	C₂×C₇	#2950	1	1	yes	characteristic
612	C₂×C₇	#3011	1	1	yes	characteristic
613	C₂×C₇	#3013	1	1	yes	characteristic
614	C₂×C₇	#3121	1	1	yes	characteristic
615	C₂×C₇	#3127	1	1	yes	characteristic
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	C₄×C₇×D₄	1	2	yes	—
623	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
624	Q₈	—	2	16	no	—
625	Q₈	—	2	2	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	2	2	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	C₄×C₇×D₄	1	4	yes	—
636	Q₈	C₄×C₇×D₄	1	4	yes	—
637	C₂×C₄	—	2	16	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
679	C₂×C₄	C₇×#120	1	2	yes	—
680	C₂×C₄	C₇×#120	1	2	yes	—
681	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
682	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
683	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
684	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
685	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
686	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
687	C₈	—	2	2	no	—
688	C₈	—	2	2	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₇	#21463	1	1	yes	characteristic, direct product factor, Sylow
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
700	C₂²	C₂×C₇×#120	1	1	yes	characteristic
701	C₂²	C₇×#525	1	1	yes	characteristic
702	C₂²	C₇×#577	1	1	yes	characteristic
703	C₂²	C₇×#578	1	1	yes	characteristic
704	C₂²	C₇×#578	1	1	yes	characteristic
705	C₂²	C₇×#578	1	1	yes	characteristic
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	4	no	—
710	C₄	—	2	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
720	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
721	C₄	C₇×#525	1	1	yes	characteristic
722	C₄	C₇×#525	1	1	yes	characteristic
723	C₂	—	4	2	no	—
724	C₂	C₄×C₇×#120	1	1	yes	characteristic
725	C₂	C₇×#2947	1	1	yes	characteristic
726	C₂	C₇×#2950	1	1	yes	characteristic
727	C₂	C₇×#3011	1	1	yes	characteristic
728	C₂	C₇×#3013	1	1	yes	characteristic
729	C₂	C₇×#3121	1	1	yes	characteristic
730	C₂	C₇×#3127	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×C₇×#441	C₂	semidirect
4. C₂×C₄×C₇×Q₁₆	C₂	semidirect
6. C₇×#1878	C₂	semidirect
7. C₇×#1878	C₂	semidirect
9. C₇×#1865	C₂	semidirect
10. C₇×#1863	C₂	semidirect
13. C₇×#1763	C₂	semidirect
14. C₄×C₇×#103	C₂	semidirect
33. C₇×#451	C₄	semidirect
64. #21463	C₇	direct (N × H)
156. C₂×#441	C₂×C₇	semidirect
157. C₂×C₄×Q₁₆	C₂×C₇	semidirect
159. #1878	C₂×C₇	semidirect
160. #1878	C₂×C₇	semidirect
162. #1865	C₂×C₇	semidirect
163. #1863	C₂×C₇	semidirect
166. #1763	C₂×C₇	semidirect
167. C₄×#103	C₂×C₇	semidirect
284. #451	C₄×C₇	semidirect
691. C₇	#21463	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#519	2
C₂×C₇×#451	2
C₂×C₇×#441	2
C₂×C₄×C₇×Q₁₆	2
C₇×#2323	2
C₇×#1878	2
C₇×#1873	2
C₇×#1865	2
C₇×#1863	2
C₇×#1854	2
C₇×#1787	2
C₇×#1763	2
C₄×C₇×#103	2
C₇×#1750	2
#21463	7

Subgroups — C7×#21463 #13198679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21463 #13198679